In the small amplitude limit, the nematic equations (REF )–() can be reduced to a
KdV equation [1]}, [2]}, [3]} on using the expansions
\(|u| = \sqrt{\rho } & = & u_{0} + \epsilon ^{2} u_{1}(\xi ,\eta ) + \epsilon ^{4}u_{2}(\xi ,\eta ) + \ldots ,  \\v & = & \epsilon ^{2}V_{1}(\xi ,\eta ) + \epsilon ^{4} V_{2}(\xi ,\eta )+ \epsilon ^{6}V_{3}(\xi ,\eta ) + \ldots ,  \\\theta & = & \frac{u_{0}^{2}}{q} + \epsilon ^{2}\theta _{1}(\xi ,\eta ) + \epsilon ^{4}\theta _{2}(\xi ,\eta )+ \epsilon ^{6}\theta _{3}(\xi ,\eta ) + \ldots \) 
